GBVE分布的参数估计

ESTIMATORS OF PARAMETERS OF GBVE DISTRIBUTION

设二元随机变量（Ｘ，Ｙ）的生存函数为可．把它称作ＧＢＶＥ（θ１，θ２，δ）．本文采用把元件和系统（串联）的定时截尾寿命试验数据综合起来进行统计分析的方法，研究ＧＢＶＥ（θ１，θ２，δ）中参数的估计及其性质．在θ１＝θ２＝θ的情况下给出了（θ，δ）的极大似然估计证明了具有强相合性和渐近正态性．在无θ１＝θ２限制时给出了（θ１，θ２，δ）的矩法估计（θ１，θ２，θ３，δ），证明了同样具有强相合性和渐近正态性．

Let the survival function of two-dimensional random variables(X, Y) be F(x,y) ￣ exp{-[(x /θ1),1/δ + (y/θ2)1/δ]δ}, 0< x,y <∞, 0<δ≤1.0<δθ1,θ2< ∞.We refer to it as GBVE(θ1,θ2,δ).In this paper, using both time-truncated life testing data of components and series systems, we study the estimators and their properties of parameters of GBVE (θ,θ1,δ). In the case of θ1=θ2=θ, we give the maximum likelihood estimator (θL,δL) of (θ,δ) and prove that (θ,δ) has strong consistency and asymptotic normality. In the case without the restriction of θ1 = θ2, we give the moment type estimator(θ1,θ2,δ) of (θ1,θ2,δ), and prove that (θ1,θ2,δ) has strong consistency and asymptotic normality, too.